Production of bottomonium-like Z_b states in e-h and ultraperipheral h-h collisions

The photoproduction of the bottomonium-like states Z_b(10610) and Z_b(10650) via γ p scattering is studied within an effective Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of Z_b states via the t-channel with π exchange. The numerical results show that the values of the total cross-sections of Z_b(10610) and Z_b(10650) can reach 0.09 nb and 0.02 nb, respectively,near the center-of-mass energy of 22 GeV. Experimental measurements and studies of the photoproduction of Z_b states near the energy region around W ■ 22 GeV are suggested. Moreover, with the help of eSTARlight and STARlight programs, we have obtained the cross-sections and numbers of events for Z_b(10610) production in electron-ion collisions(EIC) and ultraperipheral collisions(UPCs). The results show that a considerable number of Z_b(10610)events can be produced in the relevant experiments on EICs and UPCs. We have also calculated the rates and kinematic distributions for γp → Z_bn in ep and pA collisions via EICs and UPCs. The results will provide an important reference for the RHIC, LHC, EIC-US, LHeC, and FCC experiments in searching for bottomonium-like Z_b states.     

Calculations of the α-decay properties of Z = 120, 122, 124, 126 isotopes

The \begin{document}$\alpha$\end{document}-decay properties of even-Z nuclei with Z = 120, 122, 124, 126 are predicted. We employ the generalized liquid drop model (GLDM), Royer's formula, and universal decay law (UDL) to calculate the \begin{document}$\alpha$\end{document}-decay half-lives. By comparing the theoretical calculations with the experimental data of known nuclei from Fl to Og, we confirm that all the employed methods can reproduce the \begin{document}$\alpha$\end{document}-decay half-lives well. The preformation factor \begin{document}$P_{\alpha}$\end{document} and \begin{document}$\alpha$\end{document}-decay energy \begin{document}$Q_{\alpha}$\end{document} show that \begin{document}$^{298,304,314,316,324,326,338,348}$\end{document}120, \begin{document}$^{304,306,318,324,328,338}$\end{document}122, and \begin{document}$^{328,332,340,344}$\end{document}124 might be stable. The \begin{document}$\alpha$\end{document}-decay half-lives show a peak at Z = 120, N = 184, and the peak vanishes when Z = 122, 124, 126. Based on detailed analysis of the competition between \begin{document}$\alpha$\end{document}-decay and spontaneous fission, we predict that nuclei nearby N = 184 undergo \begin{document}$\alpha$\end{document}-decay. The decay modes of \begin{document}$^{287-339}$\end{document}120, \begin{document}$^{294-339}$\end{document}122, \begin{document}$^{300-339}$\end{document}124, and \begin{document}$^{306-339}$\end{document}126 are also presented.     

Relative probabilities of breakup channels in reactions of ~(6,7)Li with ~(209)Bi at energies around and above the Coulomb barrier

Coincidence measurements of breakup fragments in reactions of~ (6,7) Li with ~(209)Bi at energies around and above the Coulomb barrier were carried out using a large solid-angle covered detector array. Through the Q values along with the relative energies of the breakup fragments, different breakup components(prompt breakups and delayed breakups) and different breakup modes(α + t, α + d, α + p, and α + α) are distinguished. A new breakup mode, α + t, is observed in ~6Li-induced reactions at energies above the Coulomb barrier. Correlations between breakup modes and breakup components as well as their variations with the incident energy are investigated. The results will help us better understand the breakup effects of weakly bound nuclei on the suppression of a complete fusion, particularly for the above-barrier energies.     

Possibility of observation of hidden-bottom pentaquark resonances in bottomonium photoproduction on protons and nuclei near threshold

We study the \begin{document}$\Upsilon(1S)$\end{document} meson photoproduction on protons and nuclei at near-threshold center-of-mass energies below 11.4 GeV (or at the corresponding photon laboratory energies \begin{document}$E_{\gamma}$\end{document} below 68.8 GeV). We calculate the absolute excitation functions for the nonresonant and resonant photoproduction of \begin{document}$\Upsilon(1S)$\end{document} mesons off protons at incident photon laboratory energies of 63-68 GeV by considering direct (\begin{document}${\gamma}p \to {\Upsilon(1S)}p$\end{document}) and two-step (\begin{document}${\gamma}p \to P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11130) \to {\Upsilon(1S)}p$\end{document}) \begin{document}$\Upsilon(1S)$\end{document} production channels within different scenarios for the nonresonant total cross section of the elementary reaction \begin{document}${\gamma}p \to {\Upsilon(1S)}p$\end{document} and for branching ratios of the decays \begin{document}$P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}$P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, and \begin{document}$P^+_b(11130) \to {\Upsilon(1S)}p$\end{document}. We also calculate an analogous function for the photoproduction of \begin{document}$\Upsilon(1S)$\end{document} mesons on the ¹²C and ²⁰⁸Pb target nuclei in the near-threshold center-of-mass beam energy region of 9.0-11.4 GeV by considering the respective incoherent direct (\begin{document}${\gamma}N \to {\Upsilon(1S)}N$\end{document}) and two-step (\begin{document}${\gamma}p \to P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11130) \to {\Upsilon(1S)}p$\end{document} and \begin{document}${\gamma}n \to P^0_b$\end{document}\begin{document}$ (11080) \to{\Upsilon(1S)}n $\end{document}, \begin{document}${\gamma}n \to P^0_b(11125) \to {\Upsilon(1S)}n$\end{document}, \begin{document}${\gamma}n \to P^0_b(11130) \to {\Upsilon(1S)}n$\end{document}) \begin{document}$\Upsilon(1S)$\end{document}) production processes using a nuclear spectral function approach. We demonstrate that a detailed scan of the\begin{document}$\Upsilon(1S)$\end{document} total photoproduction cross section on proton and nuclear targets in the near-threshold energy region in future high-precision experiments at the proposed high-luminosity electron-ion colliders EIC and EicC in the US and China should provide a definite result for or against the existence of the nonstrange hidden-bottom pentaquark states\begin{document}$P_{bi}^+$\end{document} and \begin{document}$P_{bi}^0$\end{document} (\begin{document}$i$\end{document}=1, 2, 3) as well as clarify their decay rates.     

Systematic study of the α decay preformation factors of the nuclei around the Z = 82, N = 126 shell closures within the generalized liquid drop model

In this study, we systematically investigate the \begin{document}$\alpha$\end{document} decay preformation factors, \begin{document}$P_{\alpha}$\end{document} , and the \begin{document}$\alpha$\end{document} decay half-lives of 152 nuclei around Z = 82, N = 126 closed shells based on the generalized liquid drop model (GLDM) with \begin{document}$P_{\alpha}$\end{document} being extracted from the ratio of the calculated \begin{document}$\alpha$\end{document} decay half-life to the experimental one. The results show that there is a remarkable linear relationship between \begin{document}$P_{\alpha}$\end{document} and the product of valance protons (holes) \begin{document}$N_p$\end{document} and valance neutrons (holes) \begin{document}$N_n$\end{document} . At the same time, we extract the \begin{document}$\alpha$\end{document} decay preformation factor values of the even–even nuclei around the Z = 82, N = 126 closed shells from the study of Sun \begin{document}${et\ al.}$\end{document} [J. Phys. G: Nucl. Part. Phys., 45: 075106 (2018)], in which the \begin{document}$\alpha$\end{document} decay was calculated by two different microscopic formulas. We find that the \begin{document}$\alpha$\end{document} decay preformation factors are also related to \begin{document}$N_pN_n$\end{document} . Combining with our previous studies [Sun \begin{document}${et\ al.}$\end{document} , Phys. Rev. C, 94: 024338 (2016); Deng \begin{document}${et\ al.}$\end{document} , ibid. 96: 024318 (2017); Deng \begin{document}${et\ al.}$\end{document} , ibid. 97: 044322 (2018)] and that of Seif \begin{document}${et\ al.,}$\end{document} [Phys. Rev. C, 84: 064608 (2011)], we suspect that this phenomenon of linear relationship for the nuclei around the above closed shells is model-independent. This may be caused by the effect of the valence protons (holes) and valence neutrons (holes) around the shell closures. Finally, using the formula obtained by fitting the \begin{document}$\alpha$\end{document} decay preformation factor data calculated by the GLDM, we calculate the \begin{document}$\alpha$\end{document} decay half-lives of these nuclei. The calculated results agree with the experimental data well.     

Running vacuum model in a non-flat universe

We investigate observational constraints on the running vacuum model (RVM) of \begin{document}$\Lambda=3\nu (H^{2}+K/a^2)+c_0$\end{document} in a spatially curved universe, where \begin{document}$\nu$\end{document} is the model parameter, \begin{document}$K$\end{document} corresponds to the spatial curvature constant, \begin{document}$a$\end{document} represents the scalar factor, and \begin{document}$c_{0}$\end{document} is a constant defined by the boundary conditions. We study the CMB power spectra with several sets of \begin{document}$\nu$\end{document} and \begin{document}$K$\end{document} in the RVM. By fitting the cosmological data, we find that the best fitted \begin{document}$\chi^2$\end{document} value for RVM is slightly smaller than that of \begin{document}$\Lambda$\end{document}CDM in the non-flat universe, along with the constraints of \begin{document}$\nu\leqslant O(10^{-4})$\end{document} (68% C.L.) and \begin{document}$|\Omega_K=-K/(aH)^2|\leqslant O(10^{-2})$\end{document} (95% C.L.). In particular, our results favor the open universe in both \begin{document}$\Lambda$\end{document}CDM and RVM. In addition, we show that the cosmological constraints of \begin{document}$\Sigma m_{\nu}=0.256^{+0.224}_{-0.234}$\end{document} (RVM) and \begin{document}$\Sigma m_{\nu}=0.257^{+0.219}_{-0.234}$\end{document} (\begin{document}$\Lambda$\end{document}CDM) at 95% C.L. for the neutrino mass sum are relaxed in both models in the spatially curved universe.     

Hadronic coupling constants of the lowest hidden-charm pentaquark state,using QCD sum rules with rigorous quark-hadron duality

In this article,we illustrate how to calculate the hadronic coupling constants of the pentaquark states with QCD sum rules based on rigorous quark-hadron quality.We then study the hadronic coupling constants of the lowest diquark-diquark-antiquark type hidden-charm pentaquark state with spin-parity J~P=1/2~-in detail,and calculate the partial decay widths.The total width Г(P_c)=14.32±3.31 MeV is compatible with the experimental value T_(P_c(4312))=9.8±2.7_(-4.5)~(+3.7) MeV from the LHCb collaboration and favors assigning the P_c(4312) to be the [ud][uc]c pentaquark state with J~P=1/2~-.The hadronic coupling constants have the relation ■,and favor the hadronic dressing mechanism.The P_c(4312) may have a diquark-diquark-antiquark type pentaquark core with the typical size of the qqq-type baryon states.The strong couplings to the meson-baryon pairs DE_c lead to some pentaquark molecule components,and the P_c(4312) may spend a rather large time as the DE_c molecular state.     

Proton-halo breakup dynamics for the breakup threshold in the ε0 → 0 limit

Proton-halo breakup behavior in the \begin{document}$ \varepsilon_0\to 0 $\end{document} limit (where \begin{document}$ \varepsilon_0 $\end{document} is the ground-state binding energy) is studied around the Coulomb barrier in the \begin{document}$ ^8{\rm{B}}+{}^{58}{\rm{Ni}} $\end{document} reaction for the first time. For practical purposes, apart from the experimental \begin{document}$ ^8{\rm{B}} $\end{document} binding energy of 137 keV, three more arbitrarily chosen values (1, 0.1, 0.01 keV) are considered. It is first shown that the Coulomb barrier between the core and the proton prevents the \begin{document}$ ^7{\rm{Be}}+p $\end{document} system from reaching the state of an open proton-halo system, which, among other factors, would require the ground-state wave function to extend to infinity in the asymptotic region, as \begin{document}$ \varepsilon_0\to 0 $\end{document}. The elastic scattering cross section, which depends on the density of the ground-state wave function, is found to have a negligible dependence on the binding energy in this limit. The total, Coulomb and nuclear breakup cross sections are all reported to increase significantly from \begin{document}$ \varepsilon_0 = 137 $\end{document} to 1.0 keV, and converge to their maximum values as \begin{document}$ \varepsilon_0\to 0 $\end{document}. This increase is mainly understood as coming from a longer tail of the ground-state wave function for \begin{document}$ \varepsilon_0\leqslant 1.0 $\end{document} keV, compared to that for \begin{document}$ \varepsilon_0 = 137 $\end{document} keV. It is also found that the effect of the continuum-continuum couplings is to slightly delay the convergence of the breakup cross section. The analysis of the reaction cross section indicates a convergence of all the breakup observables as \begin{document}$ \varepsilon_0\to 0 $\end{document}. These results provide a better sense of the dependence of the breakup process on the breakup threshold.     

Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei

In the present work, based on the Wentzel-Kramers-Brillouin (WKB) theory, considering the cluster preformation probability (\begin{document}$ P_{c} $\end{document}), we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from ²²¹Fr to ²⁴²Cm. When the mass number of the emitted cluster \begin{document}$ A_{c} $\end{document} \begin{document}$ < $\end{document} 28, \begin{document}$P_{c} $\end{document} is obtained by the exponential relationship of \begin{document}$ P_{c} $\end{document} to the α decay preformation probability (\begin{document}$ P_{\alpha} $\end{document}) proposed by R. Blendowskeis \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. Lett. 61, 1930 (1988)], while \begin{document}$ P_{\alpha} $\end{document} is calculated through the cluster-formation model (CFM). When \begin{document}$ A_{c} $\end{document} \begin{document}$ \ge $\end{document} 28, \begin{document}$ P_{c} $\end{document} is calculated through the charge-number dependence of \begin{document}$ P_{c} $\end{document} on the decay products proposed by Ren \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. C 70, 034304 (2004)]. The half-lives of cluster radioactivity have been calculated by the density-dependent cluster model [Phys. Rev. C 70, 034304 (2004)] and by the unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)]. For comparison, a universal decay law (UDL) proposed by Qi \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both α decay and cluster radioactivity proposed by Santhosh [J. Phys. G: Nucl. Part. Phys. 35, 085102 (2008)], and a unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our work, Ni's formula , and the UDL can well reproduce the experimental data and are better than those of Santhosh's model. In addition, we extend this model to predict the half-lives for 51 nuclei, whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.     

Emission time sequence of neutrons and protons as probes of α-clustering structure

Neutron–proton momentum correlation functions are constructed from a three-body photodisintegration channel, i.e., core\begin{document}$ + n + p$\end{document}, and used to explore the spatial-time information of the non-clustering Woods–Saxon spherical structure as well as the \begin{document}$\alpha$\end{document}-clustering structures of \begin{document}$^{12}{\rm{C}}$\end{document} or \begin{document}$^{16}{\rm{O}}$\end{document} based on an extended quantum molecular dynamics model. The emission time sequence of neutrons and protons is indicated by the ratio of velocity-gated neutron–proton correlation functions, demonstrating its sensitivity to \begin{document}$\alpha$\end{document}-clustering structures. This work sheds light on a new probe for \begin{document}$\alpha$\end{document}-clustering structures.     

Evolution of intrinsic nuclear structure in medium mass even-even Xenon isotopes from a microscopic perspective

In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate \begin{document}$\gamma$\end{document}-vibrational bands in transitional nuclei of \begin{document}$^{118-128}{\rm{Xe}}$\end{document}. We report that each triaxial intrinsic state has a \begin{document}$\gamma$\end{document}-band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the \begin{document}$\gamma$\end{document}-vibrational band are calculated.     

Investigating S-wave bound states composed of two pseudoscalar mesons

In this study, we systematically investigated two-pseudoscalar meson systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations. By solving the Bethe-Salpeter equation numerically with the kernel containing the one-particle exchange diagrams, we found that the \begin{document}$ K\bar{K} $\end{document}, \begin{document}$ DK $\end{document}, \begin{document}$ B\bar{K} $\end{document}, \begin{document}$ D\bar{D} $\end{document}, \begin{document}$ B\bar{B} $\end{document}, \begin{document}$ BD $\end{document}, \begin{document}$ D\bar{K} $\end{document}, \begin{document}$ BK $\end{document}, and \begin{document}$ B\bar{D} $\end{document} systems with \begin{document}$ I=0 $\end{document} can exist as bound states. We also studied the contributions from heavy meson (\begin{document}$ J/\psi $\end{document} and \begin{document}$\Upsilon $\end{document}) exchanges and found that the contributions from heavy meson exchanges cannot be ignored.     

Analysis of the strong decays of Pc(4312) as a pentaquark molecular state with QCD sum rules

In this article, we tentatively assign \begin{document}$P_c(4312)$\end{document} to be the \begin{document}$\bar{D}\Sigma_c$\end{document} pentaquark molecular state with the spin-parity \begin{document}$J^P={\frac{1}{2}}^-$\end{document} , and discuss the factorizable and non-factorizable contributions in the two-point QCD sum rules for the \begin{document}$\bar{D}\Sigma_c$\end{document} molecular state in detail to prove the reliability of the single pole approximation in the hadronic spectral density. We study its two-body strong decays with the QCD sum rules, and special attention is paid to match the hadron side with the QCD side of the correlation functions to obtain solid duality. We obtain the partial decay widths \begin{document}$\Gamma\left(P_c(4312)\to \eta_c p\right)=0.255\,\,{\rm{MeV}}$\end{document} and \begin{document}$\Gamma\left(P_c(4312)\to J/\psi p\right)=9.296^{+19.542}_{-9.296}\,\,{\rm{MeV}}$\end{document} , which are compatible with the experimental value of the total width, and support assigning \begin{document}$P_c(4312)$\end{document} to be the \begin{document}$\bar{D}\Sigma_c$\end{document} pentaquark molecular state.     

Revisiting radiative leptonic B decay

In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist \begin{document}$B$\end{document}-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors \begin{document}$F_{A,V}$\end{document} in the \begin{document}$B \to \gamma \ell\nu$\end{document} decay at leading power in \begin{document}$\Lambda/m_b$\end{document}. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by \begin{document}$1/E_\gamma$\end{document} and \begin{document}$1/m_b$\end{document}), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data.     

Revisiting D-meson twist-2, 3 distribution amplitudes

Owing to the significant difference between the experimental measurements and the theoretical predictions of the standard model (SM) for the value of \begin{document}$ {\cal{R}}(D) $\end{document} of the semileptonic decay \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}, researchers speculate that this decay may be evidence of new physics beyond the SM. Usually, the D-meson twist-2, 3 distribution amplitudes (DAs) \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document} , and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document} are the main error sources when perturbative QCD factorization and light-cone QCD sum rules are used to study \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}. Therefore, it is important to obtain more reasonable and accurate behaviors for these DAs. Motivated by our previous work [Phys. Rev. D 104, no.1, 016021 (2021)] on pionic leading-twist DA, we revisit D-meson twist-2, 3 DAs \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document}, and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document}. New sum rule formulae for the \begin{document}$\xi $\end{document}-moments of these three DAs are suggested for obtaining more accurate values. The light-cone harmonic oscillator models for the DAs are improved, and their parameters are determined by fitting the values of ξ-moments via the least squares method.     

New behaviors of α-particle preformation factors near doubly magic 100Sn

The \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei above doubly magic nuclei \begin{document}$ ^{100} $\end{document}Sn and \begin{document}$ ^{208} $\end{document}Pb are investigated within the generalized liquid drop model. The results show that the \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei near self-conjugate doubly magic \begin{document}$ ^{100} $\end{document}Sn are significantly larger than those of analogous nuclei just above \begin{document}$ ^{208} $\end{document}Pb, and they will be enhanced as the nuclei move towards the \begin{document}$ N = Z $\end{document} line. The proton–neutron correlation energy \begin{document}$ E_{p-n} $\end{document} and two protons–two neutrons correlation energy \begin{document}$ E_{2p-2n} $\end{document} of nuclei near \begin{document}$ ^{100} $\end{document}Sn also exhibit a similar situation, indicating that the interactions between protons and neutrons occupying similar single-particle orbitals could enhance the \begin{document}$ \alpha $\end{document}-particle preformation factors and result in superallowed \begin{document}$ \alpha $\end{document} decay. This also provides evidence of the significant role of the proton–neutron interaction on \begin{document}$ \alpha $\end{document}-particle preformation. Also, the linear relationship between \begin{document}$ \alpha $\end{document}-particle preformation factors and the product of valence protons and valence neutrons for nuclei around \begin{document}$ ^{208} $\end{document}Pb is broken in the \begin{document}$ ^{100} $\end{document}Sn region because the \begin{document}$ \alpha $\end{document}-particle preformation factor is enhanced when a nucleus near \begin{document}$ ^{100} $\end{document}Sn moves towards the \begin{document}$ N = Z $\end{document} line. Furthermore, the calculated \begin{document}$ \alpha $\end{document} decay half-lives fit well with the experimental data, including the recent observed self-conjugate nuclei \begin{document}$ ^{104} $\end{document}Te and \begin{document}$ ^{108} $\end{document}Xe [Phys. Rev. Lett. 121, 182501 (2018)].     

Fine tuning problem of the cosmological constant in a generalized Randall-Sundrum model

To solve the cosmological constant fine tuning problem, we investigate an \begin{document}$(n+1)$\end{document}-dimensional generalized Randall-Sundrum brane world scenario with two \begin{document}$(n-1)$\end{document}-branes instead of two 3-branes. Adopting an anisotropic metric ansatz, we obtain the positive effective cosmological constant \begin{document}$\Omega_{\rm eff}$\end{document} of order \begin{document}$10^{-124}$\end{document} and only require a solution \begin{document}$\simeq50-80$\end{document}. Meanwhile, both the visible and hidden branes are stable because their tensions are positive. Therefore, the fine tuning problem can be solved quite well. Furthermore, the Hubble parameter \begin{document}$H_{1}(z)$\end{document} as a function of redshift \begin{document}$z$\end{document} is in good agreement with the cosmic chronometers dataset. The evolution of the universe naturally shifts from deceleration to acceleration. This suggests that the evolution of the universe is intrinsically an extra-dimensional phenomenon. It can be regarded as a dynamic model of dark energy that is driven by the evolution of the extra dimensions on the brane.     

P-wave contributions to B_((s))→ψKπ decays in perturbative QCD approach

We study the quasi-two-body decays B_((s)) ψ[K~*(892) K~*(1410) K~*(1680)] ψKπ by employing the perturbative QCD(PQCD) factorization approach, where the charmonia ψ represents J/ψ and ψ(2S). The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude(DA) Φ_(Kπ)~P, which comprises important final state interactions between the kaon and pion in the resonant region. Relativistic Breit-Wigner formulas are adopted to parameterize the time-like form factor F_(Kπ) appearing in the kaon-pion DAs. The SU(3) flavor symmetry breaking effect resulting from the mass difference between the kaon and pion is taken into account,which makes significant contributions to the longitudinal polarizations. The observed branching ratios and the polarization fractions of B_((s)) ψK~*(892) ψKπ are accommodated by tuning hadronic parameters for the kaon-pion DAs. The PQCD predictions for B_((s)) ψ[K~*(1410) K~*(1680)] ψKπ modes from the same set of parameters can be tested by precise data obtained in the future from LHCb and Belle Ⅱ experiments.     

Reduction of PDF uncertainty in the measurement of the weak mixing angle at the ATLAS experiment

We investigate the parton distribution function(PDF) uncertainty in the measurement of the effective weak mixing angle sin ~2θ_(eff)~l at the CERN Large Hadron Collider(LHC).The PDF-induced uncertainty is large in proton-proton collisions at the LHC due to the dilution effect.The measurement of the Drell-Yan forward-backward asymmetry(AFB) at the LHC can be used to reduce the PDF uncertainty in the sin~2θ_(eff)~l measurement.However,when including the full mass range of lepton pairs in the A_(FB) data analysis,the correlation between the PDF updating procedure and the sin~2θ_(eff)~l extraction leads to a sizable bias in the obtained sin ~2θ_(eff)~l value.From our studies,we find that the bias can be significantly reduced by removing Drell-Yan events with invariant mass around the Z-pole region,while most of the sensitivity in reducing the PDF uncertainty remains.Furthermore,the lepton charge asymmetry in the Wboson events as a function of the rapidity of the charged leptons,A_±(η_l),is known to be another observable which can be used to reduce the PDF uncertainty in the sin~2θ_(eff)~l measurement.The constraint from A_±(η_l)is complementary to that from A_(FB),and thus no bias affects the sin~2θ_(eff)~l extraction.The studies are performed using the error PDF Updating Method Package(ePump),which is based on Hessian updating methods.In this article,the CT14 HERA2 PDF set is used as an example.     

Nuclear mass parabola and its applications

We propose a method for extracting the properties of the isobaric mass parabola based on the total doubleβ-decay energies of isobaric nuclei.Two important parameters of the mass parabola,the location of the most β-stable nuclei Z_A and the curvature parameter b_A,are obtained for 251 A values,based on the total double β-decay energies of nuclei compiled in the AME2016 database.The advantage of this approach is that the pairing energy term P_A caused by the odd-even variation can be removed in the process,as well as the mass excess M(A,Z_A) of the most stable nuclide for the mass number A,which are employed in the mass parabolic fitting method.The Coulomb energy coefficient a_c=0.6910 MeV is determined by the mass difference relation for mirror nuclei,and the symmetry energy coefficient is also studied by the relation a_(sym)(A)=025 b_AZ_A.